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WO2000054198A2 - Gestion des risques sur des marches concernant des utilites distribuees via un reseau - Google Patents

Gestion des risques sur des marches concernant des utilites distribuees via un reseau Download PDF

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Publication number
WO2000054198A2
WO2000054198A2 PCT/US2000/006116 US0006116W WO0054198A2 WO 2000054198 A2 WO2000054198 A2 WO 2000054198A2 US 0006116 W US0006116 W US 0006116W WO 0054198 A2 WO0054198 A2 WO 0054198A2
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Prior art keywords
network
market
price
prices
instruments
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PCT/US2000/006116
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English (en)
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WO2000054198A8 (fr
Inventor
Fernando L. Alvarado
Rajesh Rajaraman
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Morgan Stanley Dean Witter & Co.
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Application filed by Morgan Stanley Dean Witter & Co. filed Critical Morgan Stanley Dean Witter & Co.
Priority to AU37329/00A priority Critical patent/AU3732900A/en
Publication of WO2000054198A2 publication Critical patent/WO2000054198A2/fr
Publication of WO2000054198A8 publication Critical patent/WO2000054198A8/fr

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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
    • G06Q40/06—Asset management; Financial planning or analysis
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
    • G06Q40/03—Credit; Loans; Processing thereof
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
    • G06Q40/04—Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange

Definitions

  • the present invention relates to financial services and more particularly to a system and method for managing risk in markets related to commodity delivery over a network.
  • the need for managing the price risk of electricity is greater than in many other markets because there is a high variation in the price of electricity over both time and space. There is a high variation in the price of electricity over time because it is difficult to store electric power, necessitating that the electricity be produced when demanded.
  • FERC transmission task force discovered that as much as 50 percent of a power transfer from Ontario Hydro to the New York Power Pool may have used transmission lines that were hundreds of miles away from the direct interconnection between the two locations.
  • a generator can hedge against the risk that the price of electricity will fall at a particular location electricity via a forward contract.
  • a power forward contract is a privately negotiated agreement between commercial parties containing a binding obligation to deliver electricity at a specified location and price.
  • a significant disadvantage of forward contracts is that the market for forward contracts can be illiquid at particular locations. Forward markets achieve higher liquidity by concentrating the market activity into a few standard locations. There are thousands of different locations in the power network but only a few locations in which any forward liquidity exists. Therefore, it may be difficult for the generator to find a willing buyer of the forward contract at an acceptable price at their specific location.
  • Futures contracts are generally standardized contracts for the delivery of a commodity (here, electricity) in the future at a price agreed upon when the contract is made. Because futures contracts are used primarily for hedging against price risk or speculating on the price of the commodity, market participants typically close out their futures contracts positions financially rather than through delivery.
  • PJM Pulnsylvania, New Jersey, and Maryland
  • PJM West the location for which a liquid forward and futures market exists is typically not the same location at which a particular market participant, such as a power generator, would like to make or take delivery
  • market participants using forward contracts to hedge their underlying positions incur basis risk because prices at different locations are not consistent. This basis risk is sometimes referred to as "Spatial Price Risk.” For example, due to congestion, the price of electricity at one location may differ from the price of electricity at the liquidly traded location.
  • TCC Transmission Congestion Contract
  • a congestion compensation contract explicitly compensates one of the parties if there is congestion on a transmission line.
  • Various kinds of congestion compensation contracts have been proposed and are known under various names.
  • TCC Transmission Congestion Contract
  • the TCC pays if there is a difference in price between the two locations, or, in other words, if there is a congested line in the power network.
  • a TCC suffers from a lack of liquidity because there are thousands of locations in the power network, but relatively few market participants interested in a particular location.
  • Stoft proposed a futures contract, not on the price of electricity at a particular location, but on an explicit congestion price for delivering electricity between two locations.
  • the explicit congestion price values the use of scarce transmission resources, such as a congestible transmission line.
  • a disadvantage of this approach is that the market for such contracts does not currently exist and, in fact, is unlikely to come into being, because market participants are used to locational prices for electricity, not congestion prices for the transmission of electricity.
  • congestion compensation contracts include a Fixed Transmission Right (FTR) available from PJM, which is a financial contract that entitles the holder to a stream of revenues (or charges) based on a reservation level and hourly energy price differences across a specific path.
  • FTR Fixed Transmission Right
  • ISO California Independent System Operator
  • FTR Firm Transmission Right
  • the markets for these and other congestion compensation contracts are not as liquid as the futures market and may be vulnerable to arbitrage.
  • spatial price variation i.e., basis risk
  • the present invention stems from the realization that the Spatial Price Risk is almost completely associated with the congestion prices of potentially congestible lines at a prospective time T in the future. From these congestion prices, the physics of the power flows dictates the pattern of locational prices of electricity within the network at the prospective time T, enabling any portfolio or combination of price risk instruments in the electricity market to be evaluated. More specifically, it is discovered that the cost/ for a portfolio y of price risk instruments with respect to a market participant's underlying position z in the market at the prospective time T, can be described by the following equation:
  • A represents distribution factors describing the physics of the power flows in the network as discussed in greater detail hereinafter
  • ⁇ represents the congestion prices of the congestible lines at the prospective time T
  • P represents the available market of price instruments (e.g. futures contracts, congestion compensation contracts, and other preferably liquid contracts in a market related to electricity)
  • F represents the current prices (for delivery at prospective time T) of the price risk instruments.
  • the market participant's Spatial Price Risk can be reduced or even eliminated by eliminating the role of ⁇ in equation (1).
  • one aspect of the invention relates to a method and software for managing risk in a market related to a commodity, such as electricity, delivered over a network.
  • Locational prices of the commodity in the market are modeled as a linear combination of congestion prices for congestible lines in the network.
  • a combination of price risk instruments for the market is produced in a proportion such that the effect of the congestion prices for the congestible lines on the locational prices of the commodity is reduced, or even eliminated.
  • Another aspect of the invention pertains to a method and software for evaluating a portfolio of price risk instruments in a market related to a commodity delivered over a network, such as electricity.
  • a plurality of distribution factors is estimated that indicates the effects on one or more congestible lines in the network due to transfers of the commodity at respective locations in the network.
  • the portfolio is then evaluated based on the estimated distribution factors.
  • Other aspects of the invention involve a method for hedging a set of underlying positions in the market and identifying arbitrage opportunities by producing a portfolio of price risk instruments for the market based on the estimated distribution factors.
  • Still another aspect of the invention is related to portfolios derived by the above described methods or to any portfolio of price risk instruments in which the price risk instruments are proportioned such that the effect of congestion prices of at least some congestible lines in the network on the prices of the commodity at locations in the network is eliminated.
  • FIG. 1 depicts an exemplary power network.
  • FIG. 2 is a flow diagram illustrating the operation of one embodiment of the present invention.
  • FIG. 3 is a flow diagram illustrating the operation of another embodiment of the present invention.
  • FIG. 4 depicts a computer system that can be used to implement an embodiment of the present invention.
  • the exemplary power network 100 comprises, for purposes of explanation, five locations or "nodes", 110, 120, 130, 140, and 150.
  • Node 110 is coupled to node 120 by transmission line 112 and to node 140 by transmission line 1 14.
  • Node 120 is further coupled to node 130 by transmission line 123, to node 140 by transmission line 124, and to node 150 by transmission line 125.
  • Nodes 130 and 140 are further coupled to node 150 by transmission lines 135 and 145, respectively.
  • transmission congestion in transmission line 114 in the direction marked by the arrow, namely from node 1 10 to node 140.
  • FIGS. 2 and 3 are flow diagrams illustrating the operation of different embodiments of the present invention, for example, to evaluate a portfolio of price risk instruments (see FIG. 2) or to generate portfolios of price risk instruments (see FIG. 3).
  • the locational prices in the network are modeled at an initial step 200 or 300, respectively, based on the physics of power flows in relation to congestible lines.
  • the present invention stems from the realization that the physics of power flows in an electric power network governs the pattern of electricity prices at the multiple locations in the electric power network when one or more distribution and/or transmission lines are congested, even at a prospective time T in the future.
  • the pattern of locational prices can be derived from a linear combination of the congestion prices and the price of electricity at one "reference" location.
  • the locational spot prices in the electric power network can be estimated by estimating the congestion prices, for example, by use of the following equation:
  • S represents the pattern of spot location prices in the power network at the prospective time T
  • A represents distribution factors describing the physics of the power flows in the network
  • ⁇ represents the prices of congestion for the congestible lines at the prospective time T.
  • A is an (/ + 1) x n sensitivity matrix, where / represents the number of congestible transmission lines, referred to as "flowgates," and n represents the number of locations or nodes in the network.
  • the first column of A describes the effect of transmission losses on transfers of electricity.
  • each entry of the first column of A equals one plus the percentage of transmission losses that occur when an incremental transfer of electricity is made between a reference location and the location corresponding to the entry.
  • the first column of A is all "ones.”
  • Each of the remaining columns of A contains Power Transfer Distribution Factors (PTDFs) corresponding to each of the flowgates.
  • PTDFs Power Transfer Distribution Factors
  • Each entry of a flowgate PTDF column is the percentage of the incremental flow in the flowgate that results from a transfer of electricity between the reference location and the location corresponding to the entry.
  • the factors can be estimated from the relative impedance of each of the transmissions, using a DC or AC load flow solution, and from sets of PTDFs available from the North American Electric Reliability Council (www.nerc.com).
  • ⁇ is an (/ + l)-dimensional vector that characterizes the congestion prices in the network, and may be based on the Lagrange multipliers corresponding to the power flow equations and flowgate congestion constraints.
  • the first entry of ⁇ is the spot price of electricity at the reference node, and the remaining entries of ⁇ are the prices of congestion with respect to the reference node of the / congestible lines.
  • a portofolio of price risk instruments is evaluated based on the model (step 202).
  • a portfolio is a set of positions to take financial advantage of particular market conditions or characteristics. The financial advantage may be to hedge against risk, in which the value of the portfolio is generally negative, or to assume risk, in which the value of the portfolio hopefully is positive.
  • a position is a specific asset or obligation traded in a market related to a commodity delivered over a network, such as the wholesale electricity market, the electricity derivatives market, and related markets.
  • a price risk instrument refers to a position taken for delivery or settlement at a prospective time T in the future in the market and may include, for example, forward contracts, futures contacts, congestion compensations contracts, such as TCCs and FTRs, price swaps, basis swaps, option contracts, and other derivative contracts.
  • the m available price risk instruments for a network may be expressed as an n x m matrix P in terms of a weighted average of the prices at the n locations in the market.
  • a futures contract for delivering power at a particular location would have a 1.0 for that location and a 0.0 elsewhere.
  • a TCC would have a 1.0 at the location where power is added and a -1.0 where power is removed.
  • P defined for the example as:
  • the market participant's underlying position in the market may be given as an n- dimensional vector z indicating the buy and sell obligations at a prospective time T in the future. Positive values in z represent net load (or buy) obligations, and negative values represent net generation (or sell) obligations. Generally, z will have non-zero values for a market participant who would like to hedge a particular underlying position, and all zeros for a speculator whose primary interest is assuming price risk.
  • the market participant's underlying position z at the prospective time T in the future may be met by taking positions x in the spot market at time T, by taking positions y with price risk instruments (e.g. in a futures market now for delivery or settlement at time T), or a combination of both.
  • z x + P y. (6)
  • HEDGING pertains to modeling the electric power network (step 300) and then generating a portfolio to manage risk, for example, by hedging, constructing new price risk instruments, and identifying low-risk arbitrage opportunities.
  • One embodiment of the invention therefore relates to hedging against the risk of an underlying position, which means reducing the price risk for fulfilling the underlying position at a prospective time T in the future.
  • the second term y'F is not subject to risk. All the spatial risk, thus, is associated with the uncertainty in the congestion price vector ⁇ .
  • the market participant takes the position z - P y in the spot market at time T. The hedge costs y'F.
  • Equation (9) may be viewed as a linear equation in y, the market participant's portfolio of price risk instruments. If m (the number of price risk instruments) is strictly less than / + 1 (one more than the number of congestible transmission lines), then there are too many equations in too few unknowns, and equation (9) will not usually be satisfied. In this case, however, the market participant may make a "partial hedge" by selecting a number of possible congestion events that is less than the number of price risk instruments. Accordingly, the market participant reduces exposure to the selected congestion events, while still remaining subject to the risk of the non-selected congested events.
  • the market participant would take a long (buy) position (2.9 MW) in the futures market at node 110 and a short (sell) position (-1.9 MW) in the futures market at node 150 for delivery or settlement at time T.
  • SYNTHETIC PRICE RISK INSTRUMENTS Hedging is generally favored by those market participants, such as utilities, that have a known underlying position in the actual commodity market in the form of power generation and load obligations against which the market participant would like to eliminate price risk.
  • the principles described herein above can also help brokers, dealers, financial institutions, and other financial services providers in offering new price risk instruments, even at locations that are not actively traded on the market.
  • a financial services provider who offers a new price risk instrument in effect creates an underlying position z in the commodity and related markets reflective of the new price risk instrument.
  • the financial services provider can use equation (9) to hedge against that new underlying position z with price risk instruments at other locations to eliminate the price risk for the financial services provider.
  • the price of the hedge will then determine the price at which the new price risk instrument should be offered.
  • the new price risk instruments may include TCCs and other congestion compensation contracts at locations that are not actively traded on the market.
  • a buyer's choice contract which grants the right to get power from any of a plurality of locations in the network, can also be constructed.
  • TCC Transmission Congestion Contract
  • Arbitrage is the purchase of various financial instruments for a given time to profit from a price discrepancy.
  • the second condition merely states that the cost of the arbitrage portfolio y is profitable.
  • the first arbitrage condition is satisfied when either the rows of P'A or the rows of P' are linearly dependent, which generally occurs when m (the number of available price risk instruments) exceeds / + 1 (one plus the number of congestible transmission lines) or exceeds n (the number of locations in the network). In other words, if there are "too many" electricity price risk instruments, then there is a possibility of arbitrage.
  • arbitrageurs are generally willing to give up the elimination of Spatial Price Risk if they can always make a profit in every congestion scenario, even when the profit is variable. Accordingly, arbitrageurs would seek to find a portfolio y such that the following generalized conditions hold for all congestion scenarios ⁇ :
  • Options and other derivative contracts differ from the previously discussed price risk instruments in that their value is not linear. For example, an option grants the right but not obligation to buy a commodity at a specified "strike" price. Thus, if the price of the commodity is less than the strike price, then the option will not be exercised unless the option holder would like to take a guaranteed loss. On the other hand, the option holder will exercise the option if the price of the commodity exceeds the strike price, because the option holder can lock in a profit. Consequently, the valuation of an option needs to take into account the expected values of the commodity prices to estimate the likelihood that the strike price will be exceeded.
  • an aspect of the present invention extends the evaluation of price risk instruments for options and other non-linear derivatives in equation (8) to account for the expected variation of congestion prices:
  • the congestion is modeled by a combination of a Wiener process and a Poisson jump process to arrive at the following analytical solution:
  • E( ⁇ ,(J)) where ⁇ , " and ⁇ , + represent the mean arrival rates of the Poisson jump and death processes, respectively, which may be obtained using moment matching techniques on probability distributions of other options, and E(u represents an expected Poisson random jump size.
  • FIG. 4 is a block diagram that illustrates a computer system 400 upon which an embodiment of the invention may be implemented.
  • Computer system 400 includes a bus 402 or other communication mechanism for communicating information, and a processor 404 coupled with bus 402 for processing information.
  • Computer system 400 also includes a main memory 406, such as a random access memory (RAM) or other dynamic storage device, coupled to bus 402 for storing information and instructions to be executed by processor 404.
  • main memory 406 such as a random access memory (RAM) or other dynamic storage device
  • Main memory 406 also may be used for storing temporary variables or other intermediate information during execution of instructions by processor 404.
  • Computer system 400 further includes a read only memory (ROM) 408 or other static storage device coupled to bus 402 for storing static information and instructions for processor 404.
  • ROM read only memory
  • a storage device 410 such as a magnetic disk or optical disk, is provided and coupled to bus 402 for storing information and instructions.
  • Computer system 400 may be coupled via bus 402 to a display 412, such as a cathode ray tube (CRT), for displaying information to a computer user.
  • An input device 414 is coupled to bus 402 for communicating information and command selections to processor 404.
  • cursor control 416 such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor 404 and for controlling cursor movement on display 412.
  • This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane.
  • One embodiment of the invention is related to the use of computer system 400 for trading. According to one embodiment of the invention, trading is provided by computer system 400 in response to processor 404 executing one or more sequences of one or more instructions contained in main memory 406. Such instructions may be read into main memory 406 from another computer-readable medium, such as storage device 410.
  • main memory 406 causes processor 404 to perform the process steps described herein.
  • processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory 406.
  • hard-wired circuitry may be used in place of or in combination with software instructions to implement the invention.
  • embodiments of the invention are not limited to any specific combination of hardware circuitry and software.
  • Non-volatile media include, for example, optical or magnetic disks, such as storage device 410.
  • Volatile media include dynamic memory, such as main memory 406.
  • Transmission media include coaxial cables, copper wire and fiber optics, including the wires that comprise bus 402. Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications.
  • RF radio frequency
  • IR infrared
  • Computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, an EPROM, a FLASH- EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read.
  • Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 404 for execution.
  • the instructions may initially be borne on a magnetic disk of a remote computer.
  • the remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem.
  • a modem local to computer system 400 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal.
  • An infrared detector coupled to bus 402 can receive the data carried in the infrared signal and place the data on bus 402.
  • Bus 402 carries the data to main memory 406, from which processor 404 retrieves and executes the instructions.
  • the instructions received by main memory 406 may optionally be stored on storage device 410 either before or after execution by processor 404.
  • Computer system 400 also includes a communication interface 418 coupled to bus 402.
  • Communication interface 418 provides a two-way data communication coupling to a network link 420 that is connected to a local network 422.
  • communication interface 418 may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line.
  • ISDN integrated services digital network
  • communication interface 418 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN.
  • LAN local area network
  • Wireless links may also be implemented.
  • communication interface 418 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.
  • Network link 420 typically provides data communication through one or more networks to other data devices.
  • network link 420 may provide a connection through local network 422 to a host computer 424 or to data equipment operated by an Internet Service Provider (ISP) 426.
  • ISP 426 provides data communication services through the worldwide packet data communication network, now commonly referred to as the "Internet” 428.
  • Internet 428 uses electrical, electromagnetic or optical signals that carry digital data streams.
  • the signals through the various networks and the signals on network link 420 and through communication interface 418, which carry the digital data to and from computer system 400, are exemplary forms of carrier waves transporting the information.
  • Computer system 400 can send messages and receive data, including program code, through the network(s), network link 420, and communication interface 418.
  • a server 430 might transmit a requested code for an application program through Internet 428, ISP 426, local network 422 and communication interface 418.
  • one such downloaded application provides for trading as described herein.
  • the received code may be executed by processor 404 as it is received, and/or stored in storage device 410, or other non-volatile storage for later execution. In this manner, computer system 400 may obtain application code in the form of a carrier wave.
  • a system, method, software, and portfolios for managing risk in markets relating to a commodity delivered over a network are described. More specifically, techniques are disclosed, wherein a market participant can construct portfolios of preferably liquid price risk instruments in specific proportions such that the price risk for the market participant's underlying position is reduced or even eliminated for contemplated congestion conditions. In addition to hedging, market participants can construct and properly evaluate new price risk instruments, as well as identify arbitrage opportunities among offered new price risk instruments whose prices are not reflective of the physics of power flows.

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Abstract

La présente invention concerne un système, un procédé, un logiciel et des portefeuilles permettant de gérer les risques sur des marchés se rapportant à une utilité livrée via un réseau. En l'occurrence, un intervenant du marché construit des portefeuilles à base d'instruments à risque de prix liquide dans des proportions qui éliminent le risque des prix spatiaux pour la position sous-jacente de l'intervenant du marché. L'invention concerne également des procédés permettant de construire et de calculer de nouveaux instruments à risque de prix et d'autres ensembles de positions, ainsi que l'identification d'opportunités d'arbitrage sur ces marchés.
PCT/US2000/006116 1999-03-11 2000-03-10 Gestion des risques sur des marches concernant des utilites distribuees via un reseau WO2000054198A2 (fr)

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US7716102B1 (en) 2010-05-11
AU3732900A (en) 2000-09-28
US7567926B2 (en) 2009-07-28
US20060026096A1 (en) 2006-02-02
WO2000054198A8 (fr) 2001-10-18
US20060026095A1 (en) 2006-02-02
US7739173B2 (en) 2010-06-15

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